The term “logos” is used
by Heraclitus for logos (in philosophy), something that later was discussed as “logic” in Hegel‘s Science of Logic.
in Freyd-Scedrov as a synonym for Heyting category;
in Joyal 08 as a synonym for quasi-category ((∞,1)-category).
In Joyal 2015 and Anel–Joyal 2019 for an object of the opposite of the category of toposes. This works on the same lines as the duality between frames and locales. There is a higher version of logos, known as an $\infty$-logos.
In Anel 2019 for a cartesian closed (infinity,1)-category with finite limits and van Kampen colimits in size bounded by some inaccessible cardinal.
Peter Freyd, Andre Scedrov, Categories, Allegories
André Joyal, Notes on Logoi, 2008 (pdf)
André Joyal, A crash course in topos theory : the big picture, lecture series at Topos à l’IHÉS, 2015 Video 1, Video 2, Video 3, Video 4.
Mathieu Anel and André Joyal, Topo-logie, preprint, 2019 (pdf)
Mathieu Anel, Descent and Univalence, talk at HoTTEST, May 2019, slides, video
Discussion of relation to taoism?:
Last revised on August 23, 2019 at 06:27:11. See the history of this page for a list of all contributions to it.